The received signal in coherent fiber-optic systems is affected by propagation impairments, e.g., polarization rotations, chromatic dispersion, polarization mode dispersion. The phase and frequency offset compensation issues in coherent fiber-optic systems are discussed, for example, by M. Kuschnerov et al in “DSP for Coherent Single-Carrier Receivers”, J. Lightwave Technol., vol. 27, no. 16, page 3614, 15 Aug. 2009. In conventional wavelength division multiplexing, WDM, optical communications systems, employing orthogonal signaling, such as Nyquist WDM, fiber impairments are compensated for by an adaptive 2D feed-forward equalizer, 2D-FFE, also known as butterfly equalizer. The equalizer is simply configured and adaptively controlled by means of a stochastic gradient algorithm that tries to minimize the mean square error, MSE, between equalized samples and transmitted symbols. In this way, the 2D-FFE minimizes the contribution of noise and inter-symbol interference, ISI, to the MSE. However, in coherent systems based on time-frequency packing, TFP, this strategy is no longer optimal. In fact, the role of the 2D-FFE should be that of compensating for fiber impairments and performing matched filtering, without trying to remove the ISI intentionally introduced by TFP. After the 2D-FFE, a maximum a posteriori probability, MAP, detector (implemented, for instance, by a Bahl, Cocke, Jelinek, Raviv, BCJR, algorithm) should take care of this ISI. Moreover, the control strategy should be adaptive and should not require prior knowledge of the transfer function of the various elements composing the transmitter (drivers, modulators, filters) and receiver (filters, photodetectors, analog-to-digital converters). Finally, the control strategy should also take care of possible interactions with the frequency-offset and phase-noise compensation algorithms.